In the case of a thin metallic slab, empirical models have been thoroughly explored. Upon the introduction of a boundary to an infinite metallic slab, a negative (begrenzung) peak is introduced at the same energy as the bulk peak, and a trailing surface peak appears. [1]} The surface peak becomes more intense with decreasing thickness, as does the negative begrenzung peak, decreasing the net bulk-plasmon amplitude. Surface modes become dominant for silver thickness between \(20\,\)  and \(10\,\) nm. This is consistent with observations in the well-validated and widely-used empirical data by Johnson and Christy [2]} as well as observations in our previous work on graphene/noble metal multilayer systems. [3]} Comparison with experimental results for very thin silver layers provides further verification of the model for a wide variety of silver metal layer thicknesses. Both bulk and surface peak locations and relative intensities for \(4\,\) nm are in excellent agreement with experimental results for EELS of \(3.4\,\) nm silver layers. [4]}
